In this work, we are interested in optimising the heuristic function for A*  [1]}, which despite the popularity of Monte Carlo tree search [2]}, [3]} is interesting due to its guarantees on optimal solution. A* is also optimally efficient in the sense that it expands the minimal number of states. Majority of prior art [4]}, [5]}, [6]}, [7]}, [8]} optimises the heuristic function by minimizing the error of the predicted cost to the goal on a training set of problem instances,The training set contains solved problem instances, where the solution should be ideally found by a search finding optimal solution, such as A* with ideally admissible heuristic function. where the error is measured by the \(\mathrm {L}_2\)  error function or its variant. The zero \(\mathrm {L}_2\)  does not guarantee the optimal efficiency of A* , hence it gives a false sense of security. Some of these deficiencies have already been pointed out in [9]}, [7]}, [11]}, [12]}.
